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Given an undirected graph with edge costs and a subset of k ≥ 3 nodes called terminals, a multiway, or k-way, cut is a subset of the edges whose removal disconnects each terminal from the others. The multiway cut problem is to find a minimum-cost multiway cut. This problem is Max-SNP hard. Recently Calinescu, Karloff, and Rabani (STOC'98) gave a novel(More)
Given a directed graph G = (V; E), a natural problem is to choose a minimum number of the edges in E such that, for any two vertices u and v, if there is a path from u to v in E, then there is a path from u to v among the chosen edges. We show that in graphs having no directed cycle with more than three edges, this problem is equivalent to Maximum Bipartite(More)
Efficient algorithms are known for computing a minimum spann.ing tree, or a shortest path. tree (with a fixed vertex as the root). The weight of a shortest path tree can be much more than the weight of a minimum spa,n-ning tree. Conversely, the distance bet,ween the root, and any vertex in a minimum spanning tree may be much more than the distance bet#ween(More)
The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. We develop the marking algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor of 2H k of optimum. (Where H k is the kth harmonic number,(More)
Time series shapelets are small, local patterns in a time series that are highly predictive of a class and are thus very useful features for building classifiers and for certain visualization and summarization tasks. While shapelets were introduced only recently, they have already seen significant adoption and extension in the community. Despite their(More)
We introduce a new technique called oblivious rounding | a variant of randomized rounding that avoids the bottleneck of rst solving the linear program. Avoiding this bottleneck yields more eecient algorithms and brings probabilistic methods to bear on a new class of problems. We give oblivious rounding algorithms that approximately solve general packing and(More)
We use Fibonacci heaps to improve a parametric shortest path algorithm of Karp and Orlin, and we combine our algorithm and the method of Schneider and Schneider's minimum-balance algorithm to obtain a faster minimum-balance algorithm. For a graph with n vertices and m edges, our parametric shortest path algorithm and our minimum-balance algorithm both run(More)
Consider the following file caching problem: in response to a sequence of requests for files, where each file has a specified size and retrieval cost, maintain a cache of files of total size at most some specified k so as to minimize the total retrieval cost. Specifically, when a requested file is not in the cache, bring it into the cache, pay the retrieval(More)